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"I am here debating you with kindness. I don't have a sword in my hand, and I am ready for your answer," according to the statement read by Barfi.

In English, Barfi told reporters gathered outside the Sotloff family's home in Miami: "Today, we grieve. This week, we mourn. But we will emerge from this ordeal ... We will not allow our enemies to hold us hostage with the sole weapons they possess, fear."

'We will not forget'

The statement came just hours after President Barack Obama said the United States will not be intimidated by the killers of two American journalists.

"Those who make the mistake of harming Americans will learn that we will not forget ... that our reach is long and that justice will be served," Obama said during a news conference in Estonia, where he was meeting with leaders of the Baltic nations.

The killing is the second beheading of an American journalist in two weeks, and the militant group said it's a result of Obama's decision to conduct airstrikes in Iraq against ISIS, which calls itself the Islamic State.

"It makes you sick to your stomach, but it again reminds you of the brutality and barbarism that is afoot in some places in the world," Hagel said. "... It won't just recede into the gray recesses of history until we stop it."

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ISIS blames Obama for Sotloff beheading00:34

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"This, as the President has said, is going to have to be a sustained effort. And it's going to take time, and it will probably go beyond even this administration to get to the point of defeat," Deputy National Security Adviser Tony Blinken told CNN's Wolf Blitzer.

Vice President Joe Biden added his own voice to the calls for justice, saying the United States will pursue the killers "to the gates of hell."

"As a nation, we are united, and when people harm Americans, we don't retreat, we don't forget," he said at an appearance near Portsmouth, New Hampshire.

"We take care of those who are grieving. And when that's finished, they should know we will follow them to the gates of hell until they are brought to justice, because hell is where they will reside. Hell is where they will reside."

The video

The video of Sotloff's execution was posted online Tuesday.

In a scene eerily similar to an earlier video of the death of U.S journalist James Foley, Sotloff kneels in the desert, dressed in an orange prison-style jumpsuit. A masked "executioner" lords over him, wielding a knife.

"I'm back, Obama, and I'm back because of your arrogant foreign policy toward the Islamic State," the executioner says. "Just as your missiles continue to strike our people, our knife will continue to strike the necks of your people."

The executioner appears to be the same person, and the location of the two killings appears to be similar, probably in or around Raqqa, one of the safest areas for ISIS, said Peter Neumann, a professor at King's College London.

"It is almost the exact same choreography," Neumann said.

The journalist speaks; the executioner speaks. Then the victim is beheaded.

In the video released Tuesday, a British hostage is shown after the beheading of Sotloff, just as Sotloff was shown in Foley's video.

British rescue attempt

The UK said it attempted to rescue one of its citizens held by ISIS "some time ago" but failed.

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UK Foreign Secretary Philip Hammond provided scant details of the rescue attempt or any other plans in the works.

"You wouldn't expect me to discuss various options that we will be considering," he said. "But I can assure you that we will look at every possible option to protect this person."

Britain echoed the same sentiment as Obama.

"This country will never give into terrorism ... a country like ours will not be cowed by these barbaric killers," Prime Minister David Cameron said.

This summer, several dozen of the most elite U.S. commandos flew into Syria but couldn't find the hostages, including Sotloff and Foley, a U.S. official told CNN last month.

'Degrade and destroy'

Speaking Wednesday, Obama addressed his much-criticized statement last week that he has no strategy on ISIS. He said he was referring to a military strategy in Syria that "might" require congressional approval.

"Our objective is clear. That is to degrade and destroy (ISIS) so it's no longer a threat," he said. "We can accomplish that. It's going to take some time, it's going to take some effort."

Obama said the world needs a regional strategy to defeat the group.

"We've been putting together a strategy that was designed to do a number of things. ... What we have to make sure is we have a regional strategy in place," he said.